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The same in every country

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(TODO: Learn and elaborate more on their respective histories and goals.)

The formula
\frac{\pi}{4} = 1 - \frac13 + \frac15 - \frac17 + \frac19 - \frac1{11} + \dots
(reminded via this post), a special case at x=1 of
\arctan x = x - \frac{x}3 + \frac{x}5 - \frac{x}7 + \dots,

was found by Leibniz in 1673, while he was trying to find the area (“quadrature”) of a circle, and he had as prior work the ideas of Pascal on infinitesimal triangles, and that of Mercator on the area of the hyperbola y(1+x) = 1 with its infinite series for \log(1+x). This was Leibniz’s first big mathematical work, before his more general ideas on calculus.

Leibniz did not know that this series had already been discovered earlier in 1671 by the short-lived mathematician James Gregory in Scotland. Gregory too had encountered Mercator’s infinite series \log(1+x) = x - x^2/2 + x^3/3 + \dots, and was working on different goals: he was trying to invert logarithmic and trigonometric functions.

Neither of them knew that the series had already been found two centuries earlier by Mādhava (1340–1425) in India (as known through the quotations of Nīlakaṇṭha c.1500), working in a completely different mathematical culture whose goals and practices were very different. The logarithm function doesn’t seem to have been known, let alone an infinite series for it, though a calculus of finite differences for interpolation for trigonometric functions seems to have been ahead of Europe by centuries (starting all the way back with Āryabhaṭa in c. 500 and more clearly stated by Bhāskara II in 1150). Using a different approach (based on the arc of a circle) and geometric series and sums-of-powers, Mādhava (or the mathematicians of the Kerala tradition) arrived at the same formula.

[The above is based on The Discovery of the Series Formula for π by Leibniz, Gregory and Nilakantha by Ranjay Roy (1991).]

This startling universality of mathematics across different cultures is what David Mumford remarks on, in Why I am a Platonist:

As Littlewood said to Hardy, the Greek mathematicians spoke a language modern mathematicians can understand, they were not clever schoolboys but were “fellows of a different college”. They were working and thinking the same way as Hardy and Littlewood. There is nothing whatsoever that needs to be adjusted to compensate for their living in a different time and place, in a different culture, with a different language and education from us. We are all understanding the same abstract mathematical set of ideas and seeing the same relationships.

The same thought was also expressed by Mean Girls:


Written by S

Tue, 2016-03-15 at 13:53:32

Posted in history, mathematics

Prefatory apprehension

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Robert Recorde’s 1557 book is noted for being the first to introduce the equals sign =, and is titled:

The Whetstone of Witte: whiche is the seconde parte of Arithmeteke: containing the extraction of rootes; the cossike practise, with the rule of equation; and the workes of Surde Nombers.

Its title page (see, see also the full book at contains this verse:

Original spelling

Though many ſtones doe beare greate price,
whetſtone is for exerſice
As neadefull, and in woorke as ſtraunge:
Dulle thinges and harde it will ſo chaunge,
And make them ſharpe, to right good vſe:
All arteſmen knowe, thei can not chuſe,
But uſe his helpe: yet as men ſee,
Noe ſharpeneſſe ſemeth in it to bee.

The grounde of artes did brede this ſtone:
His vſe is greate, and moare then one.
Here if you lift your wittes to whette,
Moche ſharpeneſſe thereby ſhall you gette.
Dulle wittes hereby doe greately mende,
Sharpe wittes are fined to their fulle ende.
Now proue, and praiſe, as you doe finde,
And to your ſelf be not vnkinde.

Modern spelling

Though many stones do bear great price,
The whetstone is for exercise
As needful, and in work as strange:
Dull things and hard it will so change
And make them sharp, to right good use:
All artsmen know they cannot choose
But use his help; yet as men see,
No sharpness seemeth in it to be.

The ground of arts did breed this stone;
His use is great, and more than one.
Here if you lift your wits to whet,
Much sharpness thereby shall you get.
Dull wits hereby do greatly mend,
Sharp wits are fined to their full end.
Now prove and praise as you do find,
And to yourself be not unkind.

Apparently the full title contains a pun (see “the cossike practise” in the title refers to algebra, as the Latin cosa apparently meaning “a thing” was used to stand for an unknown, abbreviated to cos — but the Latin word cos itself means a grindstone.

The author again reminds readers not to blame his book, at the end of his preface:

To the curiouſe ſcanner.

If you ought finde, as ſome men maie,
That you can mende, I ſhall you praie,
To take ſome paine ſo grace maie ſende,
This worke to growe to perfecte ende.

But if you mende not that you blame,
I winne the praiſe, and you the ſhame.
Therfore be wiſe, and learne before,
Sith ſlaunder hurtes it ſelf moſte ſore.

Authors are either anxious about how their book is received, or make sure to be pointedly uncaring.

Sir Arthur Conan Doyle, in a mostly forgettable volume of poetry (Songs of the Road, 1911), begins:

If it were not for the hillocks
   You’d think little of the hills;
The rivers would seem tiny
   If it were not for the rills.
If you never saw the brushwood
   You would under-rate the trees;
And so you see the purpose
   Of such little rhymes as these.

Kālidāsa of course begins his Raghuvaṃśa with a grand disclaimer:

kva sūryaprabhavo vaṃśaḥ kva cālpaviṣayā matiḥ /
titīrṣur dustaram mohād uḍupenāsmi sāgaram // Ragh_1.2 //

mandaḥ kaviyaśaḥ prārthī gamiṣyāmy upahāsyatām /
prāṃśulabhye phale lobhād udbāhur iva vāmanaḥ // Ragh_1.3 //

atha vā kṛtavāgdvāre vaṃśe ‘smin pūrvasūribhiḥ /
maṇau vajrasamutkīrṇe sūtrasyevāsti me gatiḥ // Ragh_1.4 //

But the most nonchalant I’ve seen, thanks to Dr. Ganesh, is this gīti by Śrīkṛṣṇa Brahmatantra Yatīndra of the Parakāla Maṭha, Mysore:

nindatu vā nandatu vā
mandamanīṣā niśamya kṛtim etām
harṣaṃ vā marṣaṃ vā
sarṣapamātram api naiva vindema

Screw you guys. :-)

Written by S

Wed, 2014-05-28 at 23:56:11

Posted in history, mathematics

New Year

with 4 comments

Some time in the last two weeks, I tried to figure out the answers to two questions:

  1. Why does the new year begin on January 1?
  2. Why does January 1 occur when it does?

That is, the history of the calendar. The former question is about the structure of the calendar, and the latter about its (arbitrary) point of origin.

I don’t have definitive answers yet (and I’m beginning to wonder if any exist); please help me if you know something.

Meanwhile, here’s what I’ve been able to piece together from reading Wikipedia. The calendar most of us use most of the time can be understood in three phases…

Phase I: The (pre-Julian) Roman calendar: before 45 BCE

The Greeks used several lunar calendars. The Romans probably inherited such a calendar, and their early calendar was a lunar one. “According to Livy, Numa’s calendar was lunisolar with lunar months and several intercalary months spread over nineteen years so that the Sun returned in the twentieth year to the same position it had in the first year.”

According to Roman tradition, Rome was founded around 753 BCE by Romulus, and Romulus “invented” the following calendar:

    Calendar of Romulus
Martius                 (31 days)
Aprilis                 (30 days)
Maius                   (31 days)
Iunius                  (30 days)
Quintilis               (31 days)
Sextilis                (30 days)
September               (30 days)
October                 (31 days)
November                (30 days)
December                (30 days)  [Total 304 days]
"Winter"                (About 61 days of winter, presumably)

Note that the names for months 5 to 10 (Quintilis to December) are just number names.

The arbitrariness of this calendar already makes no sense, but let’s start with it. We have to start somewhere.

In 713 BCE, Numa divided the winter into two months named Ianuarius and Februarius. Also, to make all the month lengths odd (considered lucky), he took away one day from each of the 30-day months.

Martius                 (31)
Aprilis                 (29)
Maius                   (31)
Iunius                  (29)
Quintilis               (31)
Sextilis                (29)
September               (29)
October                 (31)
November                (29)
December                (29)
Ianuarius               (29)	
Februarius              (28) [Total 355 days]

[Apparently by 450 BCE, the civil calendar had also been changed to start with Ianuarius, so half the month names became misnomers. So here’s where the answer to the first question should come from: why was the calendar changed to start with January/Ianuarius instead of March/Martius?]

February was actually two parts of odd number of days each: Part 1, 23 days, ended with Terminalia (and so did the religious year), and then there was a remaining part of 5 days. From time to time, an intercalary month of 27 days (subsuming the last 5, so only 22 additional days) was added. (So the leap year had 377 or 378 days.) So far the months were still more or less lunar, it appears.

Because the true length of a year is roughly halfway between 355 and 377, the intercalary month was needed roughly every alternate year. Adding the intercalary month was left to the Pontifex Maximus, a pontiff in charge of such things.

However, since the Pontifices were often politicians, and because a Roman magistrate’s term of office corresponded with a calendar year, this power was prone to abuse: a Pontifex could lengthen a year in which he or one of his political allies was in office, or refuse to lengthen one in which his opponents were in power. If too many intercalations were omitted, as happened after the Second Punic War and during the Civil Wars, the calendar would drift rapidly out of alignment with the tropical year. Moreover, because intercalations were often determined quite late, the average Roman citizen often did not know the date, particularly if he were some distance from the city. For these reasons, the last years of the pre-Julian calendar were later known as “years of confusion”. The problems became particularly acute during the years of Julius Caesar’s pontificate before the reform, 63–46 BC, when there were only five intercalary months, whereas there should have been eight, and none at all during the five Roman years before 46 BC. For example, Caesar crossed the Rubicon on January 10, 49 BC of the official calendar, but the official calendar had drifted so far away from the seasons that it was actually mid-autumn.


Eventually Julius Caesar became Pontifex Maximus, and reformed the calendar into the Julian calendar in 45 BCE. “The reform was intended to correct [the above] problem permanently, by creating a calendar that remained aligned to the sun without any human intervention.”

Phase II: the Julian calendar (45 BCE to some time after 1582 CE)

The Julian Calendar: Eventually Julius Caesar became Pontifex Maximus, and in 45 BCE, “called in the best philosophers and mathematicians of his time” and reformed the calendar into the Julian calendar. He decided to approximate the tropical year, and so it became a calendar of 365 days with a leap year added to February (still the last month of the religious calendar?) every four years. So a year became exactly 365.25 days on average.

Somewhere here is where one should look for the answer to the second question: what about the start of the year?

“A passage in Macrobius has been interpreted to mean that Caesar decreed that the first day of the new calendar began with the new moon which fell on the night of 1/2 January 45 BC. However, more recent studies of the manuscripts have shown that the word on which this is based, which was formerly read as lunam, should be read as linam, meaning that Macrobius was simply stating that Caesar published an edict giving the revised calendar.”

Ah, if the new moon explanation were correct, it would have answered the second question! So close.

In any case, this wasn’t the end. “the pontifices apparently misunderstood the algorithm for leap years. They added a leap day every three years, instead of every four years. […] After 36 years, this resulted in three too many leap days. Augustus remedied this discrepancy by restoring the correct frequency. He also skipped three leap days in order to realign the year. Once this reform was complete—after AD 8 at the latest—the Roman calendar was the same as the Julian proleptic calendar.”

Ah, finally! The year is fixed. Sort of.

The solstices and the equinoxes were now: 25 December, 25 March, 24 June, 24 September.

Quintilis was renamed Iulius after Iulius Caesar, and Sextilis was renamed Augustus after his successor Augustus Caesar. (Incidentally, these were not the only months to be renamed, just the only renamings to survive: “Caligula renamed September (“seventh month”) as Germanicus; Nero renamed Aprilis (April) as Neroneus, Maius (May) as Claudius and Iunius (June) as Germanicus; and Domitian renamed September as Germanicus and October (“eighth month”) as Domitianus. At other times, September was also renamed as Antoninus and Tacitus, and November (“ninth month”) was renamed as Faustina and Romanus. Commodus was unique in renaming all twelve months after his own adopted names […]” So apparently the trick in getting a month named after you is to do the renaming when the calendar is in flux, not after it’s been fixed.

Phase III: the Gregorian calendar: a few years after 1582 to today

The Gregorian calendar is what we use today, more or less.

The Julian calendar’s average of 365.25 days a year instead of about 365.2425 days a year is about 11 minutes extra each year, or about 3 days extra every 4 centuries. So the year had drifted, which had to be corrected, and in future, 3 leap days had to be removed every 4 centuries. Pope Gregory decreed this in 1582, though it took many countries a few centuries to take (or be forced to take) him seriously. This explains the “century years are not leap years unless divisible by 400” rule. Of course, Gregory’s calculation also wasn’t entirely perfect, but it’s handled nowadays by adding leap seconds etc. to the official clocks, and most of us aren’t even aware of it. (This is a mess, which David Madore has written about here.) When the calendar was introduced, it also dropped 10 days, and those who switched centuries later had to drop 10/11/12/13 days.

That’s about all of the history I have time for right now…
(It seems the answer to starting on 1 January may have something to do with some consul’s decision on when to start; the 2nd question is harder.)

Bonus: Why Christmas is on December 25th. The popular explanation is that it was a pagan winter-solstice festival that was appropriated, but according to some Christians, only the festival is pagan, not necessarily the date.

Written by S

Mon, 2011-01-10 at 15:13:07

Posted in history, unfinished

Don’t mess with a genius

with 7 comments

Or: What happens when Newton’s laws are violated

Recently, I read a book called Newton and the Counterfeiter, subtitled The Unknown Detective Career of the World’s Greatest Scientist. It focuses on an awesome phase of Isaac Newton’s later career that, like his pursuits in alchemy, gets little mention in most accounts. The story, of Newton’s job as Warden of the Mint and his efforts bringing criminals to justice, contains many elements of a modern crime thriller: including an ingenious arch-adversary, Newton visiting the gin houses of London in disguise, personally interrogating suspects, playing good cop–bad cop, and using every trick in the book, before the book had been written. The story begins, as many of them do, at the beginning.

The beginning

Isaac Newton, 55 years old and just recovered from his nervous breakdown, was looking for a post in the city (London), having lived in the village of Cambridge ever since his student days. As a Great Man now, he had already been rewarded with a seat in parliament (the only thing ever recorded spoken by him is a request to close the window), but it appeared harder to get him a job. Finally, his friends pulled the right strings, and Newton moved in as Warden of the Mint in 1696.

The job was meant to be a sinecure (he had been promised that the position “has not too much business to require more attendance than you may spare”), and no one expected him to do anything special. Today though, we can look back and confidently say that Newton is the greatest Warden the Mint ever had. Unfortunately, this is not saying much, because it appears Newton is also the only good Warden the Mint ever had.

The Mint

The Royal Mint at the time had two officials in charge, both appointed by the king and with no well-defined hierarchy between them. The Warden of the Mint, with a salary of 400-odd pounds a year, was in charge of the Mint’s facilities, and the Master of the Mint, with a salary of 600 pounds a year plus (more substantial) a percentage of every coin made, was in charge of the actual production of new coins.

When Newton moved in as Warden, the Master was the notoriously corrupt and incompetent Thomas Neale, who was so lost in his gambling habit and his numerous enterprises that the operations of the Mint were, well, not in mint condition.

This was a bad time, because counterfeiting, clipping, and arbitrage had weakened the economy to the extent that there was a shortage of cash everywhere, most tax payments and trade had stopped, panic was rising, and civil war was imminent.


Counterfeiting was easy money, and everyone took to it. The government declared it high treason, a hanging offence, but this only made juries more reluctant to hang their peers. Of those counterfeiters who were brought to trial, many escaped conviction, even one of them through a wonderful incompetence defence:

[I]nept counterfeiters attempting to exploit the currency crisis supplied the Old Bailey with a constant diet of rapidly dispatched defendants. Perhaps the most spectacular display of incompetence came from an unnamed “inhabitant of the parish of St. Andrews Holbourn,” brought to trial accused of copying French coins. His work was astonishingly awful, and he was acquitted, the jury accepting his rather bold argument that the poor quality of his work confirmed that “he had tryed to Coin with Pewter as aforesaid for Diversion, or the like, but never was concerned in Coining any manner of Money.” Few others tried this defense.

The Great Recoinage: Newton takes over

Faced with no alternative, the government had decided that the Mint would recoin everything — the Great Recoinage was to take place. It aimed to melt and restrike, in three years, more coins than it had produced in three decades. How anyone expected it to happen with Neale in charge of it is a mystery. As the recoinage began, it quickly turned into a farce, and it was clear to everyone that it would be an impossible task.

Newton saw what was happening, and couldn’t stand it. He read up on the history of the Mint, studied its operations, studied Neale, accumulated all the knowledge necessary, and somehow intimidated and pushed Neale aside in a bloodless coup, and took over the Great Recoinage himself. He streamlined the production, conducting probably one of the earliest “time-and-motion studies” (he synchronized workers’ operations to the rate of their heartbeat), running the mint from 4am to midnight, and finished the “clearly impossible task” ahead of schedule.

Warden duty

Newton's unusual coat of arms

After saving the country from economic ruin, by doing something that wasn’t even his own job, Newton finally turned to a duty that his post actually came with — protecting the currency, by “enforcing the King’s law in and around London for all crimes committed against the currency”. This meant doing a policeman’s work — or rather, that of “a criminal investigator, interrogator, and prosecutor rolled into one”. He found the idea distasteful, not to mention the kind of men he would have to come in contact with, and requested that this be assigned to someone else, but when his request was denied he turned to the task in all seriousness.

Despite having hardly been a man of the world until then, he very quickly figured out what he had to do, better than anyone else had done. (In the mere four years he was Warden, he got dozens of counterfeiters hanged.)

He descended into the underworld … hiring men to go undercover, interrogating suspects, planting informers in prisons, the works. To avoid issues of jurisdiction he got himself appointed Justice of the Peace for nineteen counties surrounding London. Most criminals (one is almost tempted to say victims) were entirely unprepared against this kind of systematic prosecution, “utterly unprepared to do battle with the most disciplined mind in Europe”.

Except one.


William Chaloner, counterfeiter, confidence trickster, and various things besides, the ingenious man who would one day challenge Sir Isaac Newton, had started small. He had set out from home — or had been thrown out — as a youth to apprentice under a nail-maker, where he learnt the basics of counterfeiting instead. Arriving in London with its oppressively exclusionary guild system, he somehow managed to survive, going through a series of professions including being a quack doctor, progressing to fortune teller, and then becoming a locator of stolen goods, at which he succeeded through the infallible trick of being the one to have stolen them in the first place.

[One of his most heinous sources of money was the following. Jacobite sedition—supporting the return of the deposed King James, over the reigning William of Orange—was treason and punishable with death, and there was a reward for those who gave up seditioners to the king. Chaloner tricked various printers into printing Jacobite propaganda, then used that as evidence to turn them in to be hanged, and claim his reward.]

Finally he turned to his true calling, that of counterfeiting. After coining a great deal of money (he once claimed to have produced more than thirty thousand pounds in his life, about four million pounds in today’s money) and getting caught a couple of times — once escaping conviction by turning informer, and the other time by coming up, along with his co-accused, with such a delightfully tangled mess of accusations and cross-accusations that everyone was let go out of confusion — he began to look for more safer avenues. He realised that for a man of his skill, making good counterfeit coins wasn’t the problem; having it untraceable back to him was. In an audacious plan, he realised that the safest place from which to pass his money was the Mint itself, and resolved to get into it.

He printed a couple of pamphlets giving advice to the government on how to prevent counterfeiting — here his expertise was all too evident — and even once gave a speech in parliament. Newton ignored him at first and denied him entry even to look at the machines in the mint, until Chaloner lost patience and decided to attack the man himself. (He alleged that the mint was making side money by participating in counterfeiting itself. The worst part was, some of these accusations were true: some dies had disappeared from the mint. Newton was put on trial and forced to defend himself, and nearly lost his job.)

Big mistake.

Newton was finally annoyed, and made it his goal to destroy him. Over the next two years, he devoted much of his life to ruining Chaloner’s. With customary ruthlessness, he set about accumulating evidence and witnesses. By now Chaloner was in custody again — bank notes and a Malt Lottery had just come into existence, and of course he counterfeited them — so he was out of the way. Newton got spies and informers planted in all the right places, he tracked down old contacts of Chaloner — friends, female coiners he’d had affairs with, wives of former associates — and subpoenaed (or just intimidated) them into giving testimony, anticipated who would try to flee to Scotland when, and prepared an impenetrable web of evidence. It is more complicated than that, and Chaloner still did his best from behind bars and the whole cat-and-mouse game has more details than I have any remaining patience to go into now :-), but you can read about them in the book. Chaloner was brought to trial. He tried every defence in succession, from pleading innocence to madness to pointing out (validly) that he was being tried by a Middlesex jury for crimes committed in London. He was convicted nevertheless, and after Newton ignored all the piteous mercy petitions he wrote, was hanged, drawn and quartered.

Newton’s later years

In 1699 the worthless Neale finally died, and Newton became Master of the Mint on Christmas Day, his 57th birthday. The responsibilities of the job had already been de facto handled by Newton for years, but Neale had gained all the proceeds from the coining — 22,000 pounds. Newton now became the only recorded Warden to become Master. Although the Great Recoinage was over, the Mint still was in production, and Newton made 3500 the first year. He finally gave up his Cambridge professorship which he had still retained, went on to become genuinely rich for the first time, and seems to have led a contented life. Much later he lost 20000 pounds in the South Sea Bubble, the world’s first stock market crash — Newton is attributed to have said: “I can calculate the movement of the stars, but not the madness of men”.

He was knighted in 1705, the first scientist to be knighted (though possibly for political reasons rather than either his science or Mint work), and died in 1727, aged 84. Despite being one of the greatest and most influential scientists of all time, he wrote:

I don’t know what I may seem to the world, but as to myself, I seem to have been only like a boy playing on the sea shore, and diverting myself in now and then finding a smoother pebble or a prettier shell than ordinary, whilst the great ocean of truth lay all undiscovered around me.

His memorial at Westminster Abbey bears was proposed to bear the inscription: “If you doubt that such a man could exist, this monument bears witness”.

More details:

Others I haven’t seen or read:
Talk by Thomas Levenson, author of the book (Running Time: 1:03:30)
Book review in The Guardian
Book review in The Telegraph
Book review in Powell’s books
Another book review in The Guardian
Story in NPR radio [23 min 23 sec]
Post by Levenson at Executed Today
Long review/book abridgement! at Chicago Boyz
The author has a blog

Written by S

Fri, 2010-06-04 at 10:25:19

New Number Nine

with 4 comments

What is the largest number?

45 billion? 24?

According to one bit of speculation, at some time, it was 8:

It is important to grasp that PIE [Proto-Indo-European] is not anything like “the first human language”, or even “the original ancestor of our languages”. [..] Nevertheless, PIE is sufficiently old that it may possibly have had properties that would make it seem not just “different” but somewhat “primitive”, if we could encounter it as an actual spoken language today. Nobody would expect PIE to have had words for “television” or “banana” — obviously. But, more interestingly, Mallory and Adams point out for instance that the PIE word for “nine” seems to derive from the word for “new”; they suggest that “nine” may originally have been called “the new number”, implying that having a name for such a big number ranked for PIE speakers as a whizzy technological breakthrough. (In English, the pronunciation of these two words has developed rather differently, but notice that in German “neun” and “neu” are closer, and in French “neuf” has both meanings.)

And Sanskrit has “nava” for both; in Hindi they become “nau” and “nayā”. Of course, the fact that the words for ‘new’ and ‘nine’ are similar or identical to each other in many Indo-European languages only means that the roots in Proto-Indo-European were similar or identical, without necessarily implying anything about the reason for it. (I find the theory implausible anyway; I’d think that larger numbers were already familiar even before the first counting words arose, and numbers probably weren’t treated with sufficient abstraction to consider the newness of a number itself.)

The passage quoted above is from Geoffrey Sampson’s PIE page, which contains a (very) short story in reconstructed Proto-Indo-European, to demonstrate what it (must have probably) sounded like.


Once there was a king. He was childless. The king wanted a son.

He asked his priest:
“May a son be born to me!”

The priest said to the king:
“Pray to the god Varuna”.

The king approached the god Varuna to pray now to the god.

“Hear me, father Varuna!”

The god Varuna came down from heaven.

“What do you want?” “I want a son.”

“Let this be so”, said the bright god Varuna.

The king’s lady bore a son.


To réecs éhest. So nputlos éhest. So réecs súhnum éwelt.

Só tóso cceutérm prcscet:
“Súhnus moi jnhyotaam!”

So cceutéer tom réejm éweuqet:
“Ihgeswo deiwóm Wérunom”.

So réecs deiwóm Werunom húpo-sesore nu deiwóm ihgeto.

“Cluttí moi, phter Werune!”

Deiwós Wérunos kmta diwós égweht.

“Qíd welsi?” “Wélmi súhnum.”

“Tód héstu”, wéuqet loukós deiwos Werunos.

Reejós pótnih súhnum gegonhe.

Several similarities both to Sanskrit and to Latin are obvious. The spelling above is artificially made “simpler” (English-like); the actual one (see Wikipedia page) has features even closer to Sanskrit:

To rḗḱs éh1est. So n̥putlos éh1est. So rēḱs súhnum éwel(e)t. Só tós(j)o ǵʰeutérm̥ (e)pr̥ḱsḱet: “Súhxnus moi ǵn̥h1jotām!” So ǵʰeutēr tom rḗǵm̥ éweukʷet: “Ihxgeswo deiwóm Wérunom”. So rḗḱs deiwóm Werunom h4úpo-sesore nu deiwóm (é)ihxgeto. “ḱludʰí moi, phater Werune!” Deiwós Wérunos km̥ta diwós égʷehat. “Kʷíd welsi?” “Wélmi súxnum.” “Tód h1éstu”, wéukʷet loukós deiwos Werunos. Rēǵós pótniha súhnum gegonh1e.

And by the time you get to Proto-Indo-Iranian, it’s almost entirely readable.

I have been looking at some comparative linguistics lately, and there’s no doubt that the essential features of the PIE reconstruction are more-or-less correct. The old view that “Sanskrit is the mother of all languages”, often repeated in India by non-linguists, is quite hard to believe after even a cursory look at the evidence available. (Note: I am not discounting the “Out of India theory”, that the Proto-Indo-European homeland was in India — my impression on that is that it seems just barely possible, though there’s no special linguistic reason to believe it, and a few not to — just pointing out that Sanskrit, in the form we have today or even in the Vedas, is most definitely the result of quite a few changes from the original PIE and it is impossible to consider it the original language.) Sanskrit is, however, one of the oldest available languages, and has preserved many features of PIE for centuries with unmatched accuracy. In the Indian context, it is the mother of all the Indo-Aryan languages (Hindi, Bengali, Gujarati, Marathi, etc.). And even the Dravidian languages (Tamil, Kannada, Telugu, Malayalam) have borrowed large parts of their vocabulary from Sanskrit, and often modeled their own grammar and literary tradition after Sanskrit.

Written by S

Thu, 2010-05-27 at 14:52:50

Posted in history, language, sanskrit

Women enter the workplace

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In 1874, less than 4% of clerical workers in the United States were women; by 1900, the number had increased to approximately 75%.
from today’s featured article on Wikipedia, to which my only contribution was cheering a bit when it was being written.

It can be argued whether C. Latham Sholes, the inventor of the (first successful) typewriter, was the saviour of women, but there can be no doubt that the typewriter was one of the most major factors in changing their role.

Relevant section on Wikipedia.

Of course, there were ugly side-effects. The entry of women was resented, and there were endless cartoons insinuating that these secretaries were cheating with their employers whose wives were at home. This was compounded by the manufacturers’ own marketing, which (as has always been the case) consisted of women in provocative pictures. The book Sexy Legs and Typewriters collects some “non-pornographic vintage erotic images” from the period.

And only a couple of decades later, when Ottmar Mergenthaler, “the second Gutenberg”, invented the linotype machine and changed typesetting forever, the printers were prepared, and banded together to prevent women from “taking their jobs”. They even succeeded, for a while.

For a brief while, when you bought a typewriter, a woman came with it.

Barbara Blackburn’s record, for being the fastest typist in the world, was using the Dvorak keyboard. Obviously. :-)

Written by S

Tue, 2010-03-02 at 20:48:52

Posted in history

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Euler, pirates, and the discovery of America

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Is there nothing Euler wasn’t involved in?!

That rhetorical question is independent of the following two, which are exceedingly weak connections.

“Connections” to piracy: Very tenuous connections, of course, but briefly, summarising from the article:

  1. Maupertuis: President of the Berlin Academy for much of the time Euler was there. His father got a license from the French king to attack English ships, made a fortune, and retired. Maupertuis is known for formulating the Principle of Least Action (but maybe it was Euler), and best known for taking measurements showing the Earth bulges at the equator as Newton had predicted, thus “The Man Who Flattened the Earth”.
  2. Henry Watson: English privateer living in India, lost a fortune to the scheming British East India Company. Wanted to be a pirate, but wasn’t actually one. Known for: translated Euler’s Théorie complette [E426] from its original French: A complete theory of the construction and properties of vessels: with practical conclusions for the management of ships, made easy to navigators. (Yes, Euler wrote that.)
  3. Kenelm Digby: Not connected to Euler actually, just the recipient of a letter by Fermat in which a problem that was later solved by Euler was discussed. Distinguished alchemist, one of the founders of the Royal Society, did some pirating (once) and was knighted for it.
  4. Another guy, nevermind.

Moral: The fundamental interconnectedness of all things. Or, connections don’t mean a thing.

The discovery of America: Columbus never set foot on the mainland of America, and died thinking he had found a shorter route to India and China, not whole new continents that were in the way. The question remained whether these new lands were part of Asia (thus, “Very Far East”) or not. The czar of Russia (centuries later) sent Bering to determine the bounds of Russia, and the Bering Strait separating the two continents was discovered and reported back: America was not part of Russia. At about this time, there were riots in Russia, there was nobody to make the announcement, and “Making the announcement fell to Leonhard Euler, still the preeminent member of the St. Petersburg Academy, and really the only member who was still taking his responsibilities seriously.” As the man in charge of drawing the geography of Russia, Euler knew a little, and wrote a letter to Wetstein, member of the Royal Society in London. So it was only through Euler that the world knew that the America that was discovered was new. This letter [E107], with others, is about the only work of Euler in English. That Euler knew English (surprisingly!) is otherwise evident from the fact that he translated and “annotated” a book on ballistics by the Englishman Benjamin Robins. The original was 150 pages long; with Euler’s comments added, it was 720. [E77, translated back into English as New principles of gunnery.]

Most or all of the above is from Ed Sandifer’s monthly column How Euler Did It.

The works of Leonhard Euler online has pages for all 866 of his works; 132 of them are available in English, including the translations from the Latin posted by graduate student Jordan Bell on the arXiv. They are very readable.

This includes his Letters to a German Princess on various topics in physics and philosophy [E343,E344,E417], which were bestsellers when reprinted as science books for a general audience. It includes his textbook, Elements of Algebra [E387,E388]. Find others on Google Books. The translations do not seem to include (among his other books) his classic textbook Introductio in analysin infinitorum [E101,E102, “the foremost textbook of modern times”], though there are French and German translations available.

Apparently, Euler’s Latin is (relatively) not too hard to follow.

Written by S

Mon, 2010-03-01 at 23:04:23

The Decline and Fall of The Decline and Fall

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(Yes, this post is written just for the title. More details would be received gratefully.)

Over a period of 17 years from 1770 to 1787, Edward Gibbon wrote The History of the Decline and Fall of the Roman Empire. It was, among other things, a mammoth history (6 volumes, 71 chapters) of the last days of Rome, which for Gibbon apparently meant several centuries. (The book covers over thirteen centuries of history; here’s an outline.)

The work received instant praise. Adam Smith’s letter to Gibbon is typical:

“I cannot express to you the pleasure it gives me to find that by the universal consent of every man of taste and learning whom I either know or correspond with, it sets you at the very head of the whole literary tribe at present existing in Europe.”

The Decline and Fall became the model for all historians that followed — including its pessimism (history as “little more than the register of the crimes, follies, and misfortunes of mankind”), its overarching narrative, and its indictment of religion.

It became a literary monument of the 18th century, and one of the works that every educated man was expected to have read, a part of every bookshelf. Churchill (“I devoured Gibbon. […] I rode triumphantly through it from end to end and enjoyed it all”), Carlyle (“how gorgeously does it swing across the gloomy and tumultuous chasm of these barbarous centuries”), Virginia Woolf (“not merely a master of the pageant and the story; he is also the critic and the historian of the mind […] We seem as we read him raised above the tumult and the chaos into a clear and rational air”)… everyone read The Decline and Fall and spoke of it in the highest terms. (Gandhi read it in jail, and considered it an inferior version of the Mahabharata.) It was read by doctors, politicians, lawyers, novelists, even Sanskrit professors.

But then times began to change. Education stopped being the reading of “classics“, and became the learning of “subjects”. Today, no one I know has read The Decline And Fall, nor considers it worth the time.

Written by S

Sun, 2009-09-06 at 02:21:27